Labour and the Liberal Democrats are "reluctant" to make changes to press regulation plans following a fresh round of cross-party talks on the issue, a source has said.

Culture Secretary Maria Miller has indicated she hopes to address media concerns about the proposals with a revised charter produced by Friday but a source said there had been no breakthrough in today's discussions.

Mrs Miller, her Labour counterpart Harriet Harman and Liberal Democrat Lord Wallace will continue their negotiations tomorrow, with the prospect of the original charter being put forward to the Privy Council if no changes can be agreed .

The source said: "Labour and the Liberal Democrats are very reluctant to make any changes that make the charter more workable for the industry.

"But we think we will convince them. We are confident that we will get there by Friday."

The Conservative source said Labour and the Lib Dems had been "dragged to the table kicking and screaming" but with further talks scheduled there was hope of progress

If changes can be agreed the document will be published on Friday, before being put to the Privy Council at the end of the month.

However, if no cross-party agreement with is reached by Friday, Mrs Miller has indicated she will press ahead with the version of the charter agreed at a late-night meeting over pizzas in Westminster on March 18 in the presence of campaign group Hacked Off.

Earlier this week, ministers rejected the industry's proposals for a new system underpinned by a Royal Charter .

Sticking points included media opposition to a free arbitration service, which publishers fear could encourage frivolous complaints, as well as the industry's desire to have representation on a new "recognition panel" to be created by the charter.

Under the cross-party plans, the job of adjudicating on complaints and imposing penalties will be performed by a new self-regulatory body set up by the industry to replace the Press Complaints Commission. The panel would be required to verify whether this watchdog was effective and genuinely independent of publishers.

However, it would be up to individual publishers to sign up to a regulator endorsed by the panel, and there is speculation that many or all of the major newspapers could opt out of the proposed system if it does not address their concerns over freedom from political interference.

Tory Mrs Miller has signalled that she is ready to give ground on two issues of concern to the press.

She is proposing to make provision for a fee for use of the arbitration service, which would be small enough to comply with Sir Brian's recommendation of a "low-cost" facility but large enough to deter speculative claims.

It is thought the charge could be in line with fees for using the small claims court, which range between £35 and £685.

She also indicated that Conservatives are ready to accept the industry drawing up a code of conduct for editors, to be approved by the independent regulator.

Sir Brian Leveson, who chaired the inquiry into press standards and ethics, has insisted that he will not interfere in the stand-off between politicians and the newspapers over regulation reforms.

The judge said it would be "totally wrong" for him to comment on the controversy surrounding proposed changes which are based on his report last year.

Giving evidence to a House of Lords select committee he also hinted that a planned second part of his inquiry, dealing with phone hacking, may never happen.

Guardian editor Alan Rusbridger said the gap between the press and the Government on regulation was "bridgeable" and "could probably be done in a day".

He told BBC Radio 4's World at One: "My sense is that the politicians are willing to amend some of the things that the press found problematic in the original charter."

Appearing before a Lords committee looking into the Inquiries Act Sir Brian told peers it would be "totally wrong" for a senior judge to step into the public domain by commenting further on press regulation.

"It would be absolutely inappropriate for me to come back into the question of my report or regulation of the press," he said.

"I was given a job to do - I was to examine the facts and make recommendations."

He said some people might think he had already laid out his findings in "tedious detail".

"I have said all that I can say on the topic. Many, many people have asked me to give speeches, keynote lectures. They come in every week," he added.

Sir Brian said he stood by what he said when he published his report last year: "I have done my best, it is for others to decide how to take this forward."

Asked outside the hearing whether he would be declining to comment when he appears before the Commons Culture, Media and Sport Committee tomorrow, the judge replied: "You will find out tomorrow, won't you?"

Sir Brian, now president of the Queen's Bench Division, said his inquiry into media standards had been "at the very edge" in terms of whether it should be headed by a judge.

He told the committee, which is looking into the operation of the Inquiries Act, that if there had not been cross-party consensus over the terms of reference the Lord Chief Justice may well have opposed a judge taking charge.

John Whittingdale, chairman of the Culture, Media and Sport Committee, said he hoped Sir Brian would not seek to avoid answering its questions tomorrow.

"I hope that is not the case," he said. "I think it would be helpful if he could express a view about where we go from here.

"A lot of these views, people are claiming that they are trying to deliver what Leveson intended to deliver."

Tory MP Mr Whittingdale added: "Having spent a great deal of time preparing a report for Parliament, I hope he would feel it is appropriate for him to answer questions.

"I personally think he could be enormously helpful in trying to identify a way forward."

Mr Whittingdale said he had not been given any indication as to whether Sir Brian would engage with the committee's questions.

"We can ask that he attend and he has agreed to do so. But it is then a matter for him as to how he answers the questions," he added.